Semiconductor Wafers Of Silicon and Method For Their Production

ABSTRACT

Semiconductor wafers of silicon are produced by pulling a single crystal growing on a phase boundary from a melt contained in a crucible and cutting of semiconductor wafers therefrom, wherein during pulling of the single crystal, heat is delivered to a center of the phase boundary and a radial profile of a ratio V/G from the center to an edge of the phase boundary is controlled, G being the temperature gradient perpendicular to the phase boundary and V being the pull rate. The radial profile of the ratio V/G is controlled so that the effect of thermomechanical stress in the single crystal adjoining the phase boundary, is compensated with respect to creation of intrinsic point defects. The invention also relates to defect-free semiconductor wafers of silicon, which can be produced economically by this method.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a division of and claims priority to U.S.application Ser. No. 12/011,713, filed Jan. 29, 2008, which, in turn,claims the benefit of U.S. provisional application Ser. No. 60/887,847,filed Feb. 2, 2007, and claims priority to German application Serial No.10 2007 005 346.2, filed Feb. 2, 2007, all of which are incorporatedherein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a method for producing semiconductor wafers ofsilicon, comprising pulling a single crystal growing on a phase boundaryfrom a melt contained in a crucible and cutting semiconductor wafersfrom the pulled single crystal, wherein heat is delivered to a center ofthe phase boundary during pulling, and a radial profile of a ratio V/Gfrom the center to an edge of the phase boundary is controlled, with Gbeing the temperature gradient perpendicular to the phase boundary and Vbeing the pull rate at which the single crystal is pulled from the melt.The invention also relates to defect-free semiconductor wafers ofsilicon, which can be produced by this method. Semiconductor wafers ofsilicon in the context of the invention are referred to as defect-freeso long as neither OSF defects, A-swirl defects, nor COP defects with asize of more than 30 nm are detectable. A method in the context of thisinvention is regarded as economically viable when, in particular, it ispossible to pull single crystals with a diameter of at least 300 mm froma crucible at a rate which is equal to at least 0.5 mm/min anddefect-free semiconductor wafers are produced in a high yield, expressedin terms of the total yield of semiconductor wafers.

2. Background Art

DE 103 39 792 A1 describes a method for producing single crystals ofsilicon which are optimized with respect to their defect properties.Attention is focused on intrinsic point defects and their agglomerates,as well as the Voronkov model which allows predictions regarding theformation of such defects. In the case of intrinsic point defects,distinction is made between interstitial silicon atoms (interstitials)and vacancies. If point defects enter supersaturation when cooling thesingle crystal, then silicon interstitials will form agglomerates whichcan be detected in the form of dislocation loops (A-swirl defects,LPITs) and smaller clusters (B-swirl defects). In the event ofsupersaturation, vacancies form vacancy agglomerates (voids) which,depending on the detection method, are referred to inter alia as COPdefects (crystal originated particles, COPs), FPD (flow patterndefects), LLS (localized light scatterers) or DSOD (direct surface oxidedefects). It is necessary to ensure that the semiconductor wafers ofsilicon have no A-swirl defects in the region relevant for producingelectronic components, and are as free as possible of COP defects whosesize lies in the range of the structure widths of the components, or areof greater size. Semiconductor wafers which fulfill these requirementsare often referred to as defect-free or perfect, even though theircrystal lattice generally contains smaller COP defects or B-swirldefects, or contains both defect types.

According to the Voronkov model, the intrinsic point defect type whichis incorporated in excess into the crystal lattice when pulling thesingle crystal depends essentially on the ratio of the pull rate V, atwhich the single crystal is pulled from the melt, and the temperaturegradient G perpendicular to the phase boundary between the growingsingle crystal and the melt. Often, instead of the temperature gradientperpendicular to the phase boundary, the axial temperature gradientdirected perpendicularly to the surface of the melt is also used inmodel calculations. If the ratio V/G falls below a critical ratio, thenan excess of silicon interstitials is created. If the critical ratio isexceeded, then vacancies predominate. If there is an excess ofvacancies, the size of the COP defects formed depends essentially on twoprocess parameters, namely the aforementioned ratio V/G and the rate atwhich the single crystal is cooled in the range of from approximately1100° C. to 1000° C. the nucleation temperature of voids. The COPdefects are therefore commensurately smaller as the ratio V/G liescloser to the critical ratio and the more rapidly the single crystal iscooled in this temperature range. In practice, attempts are thereforemade to control the two process parameters when pulling the singlecrystal, so that the defects created by supersaturation of vacanciesremain small enough not to interfere with the production of electroniccomponents. Since the structure widths of the components decrease witheach generation, the defect size which can still be tolerated decreasesaccordingly.

Owing to corrosion of the crucible, usually consisting of quartz, oxygenwill enter the melt. The oxygen forms small so-called precipitates inthe single crystal (as grown bulk micro defects, BMDs). These aredesirable to a certain extent because they can bind (getter) metallicimpurities to themselves, and thus can be used in order to move suchcontaminants away from the region of the surface into the interior(bulk) of the semiconductor wafer.

If the single crystal is pulled under conditions in which the ratio V/Glies only slightly above the critical ratio, then the interaction ofvacancies and oxygen atoms also leads to the formation of nuclei, whichgive rise to OSF defects (oxidation induced stacking faults). Thepresence of a zone with such nuclei (OSF zone) is usually detected bysubjecting a semiconductor wafer, cut from the single crystal, tooxidation in wet oxygen at about 1100° C. for a few hours so that OSFdefects are formed. Since this defect type is likewise detrimental tothe functional integrity of electronic components, endeavors are made tosuppress OSF formation, for example by reducing the concentration ofoxygen in the melt so that less oxygen is incorporated into the singlecrystal than would be necessary in order to form OSF defects. The OSFzone can also be avoided by modifying the ratio V/G, for example byusing higher or lower pull rates. The formation of OSF nuclei canmoreover be reduced by higher cooling rates (in the temperature range ofprecipitation around 900° C.). It is furthermore known that in order toavoid OSF defects, it is advantageous for the single crystal to containa small concentration of hydrogen.

Particular difficulties in controlling the ratio V/G result from thefact that the single crystal usually cools faster at the edge than atthe center, so that the ratio V/G decreases from the center toward theedge. Despite corresponding control, this can lead to unacceptably largeCOP defects being formed at the center and/or A-swirl defects in theedge region. The dependency of G on the radial position r, G(r), musttherefore be taken into account, especially when defect-freesemiconductor wafers of silicon with sizeable diameters are to beproduced economically.

In the aforementioned DE 103 39 792 A1, it is proposed to induce atransport of heat directed from below toward the center of the phaseboundary. This is intended to achieve two effects. On the one hand, theincrease in the temperature gradient G concomitant with the heattransport is intended to make it possible to increase the pull rate Vcorrespondingly, without defects therefore being generated. On the otherhand, it is intended to homogenize i.e. equalize the radial profile ofthe ratio V/G, so that it varies as little as possible from the centerto the edge of the phase boundary and lies as close as possible to thecritical ratio. With this strategy, it is feasible to producedefect-free semiconductor wafers with a diameter of 300 mm, in whichcase the single crystal can be pulled at a rate of 0.36 mm/min.

U.S. Pat. No. 6,869,478 B2 discloses that a phase boundary curved in thedirection of the single crystal generates a temperature gradient whichis steepest perpendicular to the phase boundary. Taking into account theVoronkov model, according to which point defects diffuse in thedirection of the temperature gradient and according to which siliconinterstitials diffuse faster than vacancies, it is furthermore disclosedthat the radial diffusion of silicon interstitials due to the curvatureof the phase boundary increases the concentration of vacancies at thecenter of the phase boundary. The ratio V/G, at which the concentrationsof vacancies and silicon interstitials correspond to each other, willtherefore be commensurately less as the phase boundary is curved morestrongly toward the single crystal.

The present inventors found that the predictions for defectdistributions, even when they take the radial distribution into account,differ commensurately more strongly from the defect distributions foundin experiments as the rate at which the single crystal is pulled isfaster, and as the diameter of the single crystal is greater.

FIG. 1 shows an extreme example of this observation. A single crystal ofsilicon with a nominal diameter of 300 mm was pulled at a high pull rateand an inhomogeneous radial profile of V/G was adjusted. In the centralregion, V/G was adjusted to be so low that the formation of A-swirldefects could be expected in this region according to the predictions ofthe Voronkov model. In fact, however, COP defects with a diameter ofmore than 30 nm were found. In the edge region, the ratio V/G wasadjusted to be so high that large COP defects should be formed there. Infact, however, A-swirl defects were found.

These results showed that the strategy hitherto followed in the priorart, of adjusting a ratio V/G whose radial profile changes as little aspossible and which corresponds as far as possible to the critical ratio,will not be successful when defect-free semiconductor wafers of siliconare to be produced economically.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to remedy thissituation by providing a method which works economically. These andother objects have been surprisingly achieved by pulling a singlecrystal growing on a phase boundary of a melt, wherein heat is deliveredto a central portion of the phase boundary, and the radial profile V/Gfrom the center to an edge of the phase boundary is controlled such thatthe effect of thermomechanical stress fields in the crystal adjoiningthe phase boundary is compensated for with respect to creation ofintrinsic point defects.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates defect inconsistencies occurring in actual growth oflarge single crystal silicon in contradiction to predicted defectpatterns with adjustment of V/G ratio radial profile to near thecritical ratio.

FIG. 2 illustrates the relationship of V/G and the magnitude ofthermomechanical stress.

FIG. 3 illustrates the relationship between V/G in the region ofcompressive stress and in the region of tensile stress and theimportance of maintaining the radial profile of V/G such that(V/G)_(t)/(V/G)_(c) is greater than 1.5.

FIG. 4 illustrates the differences between one embodiment of a subjectinvention wafer and prior art wafers with respect to attitude angle.

FIG. 5 illustrates a preferred axial temperature profile in accordancewith one embodiment of the present invention.

FIGS. 6 a and 6 b respectively illustrate the relationship between theradial profile of the temperature gradient G an the magnitude of thethermomechanical stress fields for a (6 a) homogenous radial profileV/G, and in inhomogeneous radial profile (6 b) in accordance with oneembodiment of the present invention.

FIG. 7 illustrates one crystal growth device suitable for use in themethod of the present invention.

FIG. 8 illustrates thermomechanical stress zones in the hot zone of agrowing crystal.

FIGS. 9 a and 9 b illustrate the attitude angle θ as revealed byphotoscan of a longitudinal section of a pulled single crystal and awafer, respectively.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The invention thus relates to a method for producing semiconductorwafers of silicon, comprising pulling a single crystal growing on aphase boundary from a melt contained in a crucible and cutting ofsemiconductor wafers from the pulled single crystal, wherein heat isdelivered to a center of the phase boundary during pulling, and a radialprofile of a ratio V/G from the center to an edge of the phase boundaryis controlled, with G being the temperature gradient perpendicular tothe phase boundary and with V being the pull rate at which the singlecrystal is pulled from the melt, wherein the radial profile of the ratioV/G is controlled so that the effect of thermomechanical stress fieldsin the single crystal adjoining the phase boundary is compensated forwith respect to the creation of intrinsic point defects.

After intensive studies, the inventors have identified thermomechanicalstress fields as a possible cause by which experimental observations maybe explained plausibly. Thermomechanical stress fields can influence theconcentration of intrinsic point defects, and therefore indirectly alsodefect formation, in a surprisingly strong way. According to theinventors' discoveries, the strength of the thermomechanical stressfields must be reduced and their effect must be compensated for in theconfiguration of the radial profile of V/G, so that in particular singlecrystals with a diameter of at least 300 mm, from which defect-freesemiconductor wafers can be produced, can be pulled economically.

K. Tanahashi and N. Inoue, Journal of Materials Science: Materials inElectronics 10 (1999) 359-363, have addressed thermomechanical stressfields in crystallizing silicon and their effect on the diffusivity andsolubility of intrinsic point defects. Although they come to theconclusion that the formation of silicon interstitials isthermodynamically promoted in the region of tensile stress and theformation of vacancies in the region of compressive stress, their modelcalculations also show that this should not exert any special effects ondefect formation.

However, the inventors have surprisingly discovered that the effect ofthe thermomechanical stress fields can be considerable, and that themagnitude of the stress fields must be limited. Furthermore, theireffect must be compensated for with respect to the creation of intrinsicpoint defects. This is expediently done by keeping the temperaturegradient G, in a region of the single crystal which is under compressivestress and adjoins a central zone of the phase boundary, greater than ina region which is under tensile stress, adjoins an edge region of thesingle crystal and extends as far as the phase boundary. The greatertemperature gradient in the region of the compressive stresses makes alarger number of silicon interstitials available, which eliminate thevacancies also present owing to the compressive stresses. The smallertemperature gradient in the region of the tensile stresses makes alarger number of vacancies available, which eliminate the siliconinterstitials also present owing to the compressive stresses. A balancedratio of vacancies and silicon interstitials is obtained as a result,which is desirable because it is a crucial prerequisite for theproduction of defect-free semiconductor wafers.

With respect to the ratio V/G, a maximally homogeneous radial profile ofV/G is not desirable, but instead an inhomogeneous radial profile with aV/G at the phase boundary in the region of the compressive stresseswhich is less than the critical ratio, and with a V/G at the phaseboundary in the region of the tensile stresses which is greater than thecritical ratio is desired. The critical ratio is the ratio V/G which isa prerequisite in the case of a flat phase boundary according to theVoronkov model, so that a defect-forming excess of point defects is notcreated.

FIG. 2 shows that the ratio V/G in the regions of the thermomechanicalstress fields must differ ever more strongly from the critical ratio asthe strength of the thermomechanical stress fields increases. Thecompressive and tensile stresses to be expected can be predicted bysimulation calculations. Commercially available programs may be used forthe calculation, for example the Flow Module program from SemiconductorTechnology Research, Inc.

FIG. 3 shows in particular that it is the ratio between V/G in theregion of the compressive stresses and V/G in the region of the tensilestresses which is important. The radial profile of V/G is preferablycontrolled so that (V/G)t/(V/G)c is at least greater than 1.5,preferably greater than 1.8 and more preferably greater than 2, where(V/G)c is the lowest ratio V/G in the region which is under compressivestress and (V/G)t is the highest ratio V/G in the region which is undertensile stress. A strategy based exclusively on the Voronkov model, suchas the one formulated for example in DE 103 39 792 A1, attempts toprovide a radial profile of V/G which is homogeneous and which differsas little as possible from the critical ratio. A strategy whichfurthermore takes into account the radial diffusivity of siliconinterstitials and is formulated, for example, in U.S. Pat. No. 6,869,478B2, discloses a radial profile of V/G in which the ratio (V/G)t/(V/G)calways lies significantly below 1.5 and may therefore be referred to asvirtually homogeneous. Although semiconductor wafers of silicon whichare regarded as defect-free in modern terms can be produced with thelatter strategies, this can only be done by methods which must beregarded as economically unviable. The present invention overcomes thisshortcoming since the inventive method makes it possible to obtaindefect-free semiconductor wafers of silicon from single crystals havinga diameter of at least 300 mm, and which are pulled economically atrates of at least 0.5 mm/min.

Such semiconductor wafers, which are also suitable as substrates forproducing epitaxial semiconductor wafers and SOI wafers, can also bereadily distinguished from defect-free semiconductor wafers of siliconwhich come from single crystals pulled in the known way, andspecifically by the radial profile of the attitude angle θ of oxygen anddopant striations. The Voronkov model predicts that single crystals fordefect-free semiconductor wafers can be pulled rapidly only if thetemperature gradient G is increased. Only in this way can the pull rateV be increased and the critical ratio V/G maintained at the same time.The increased heat supply means that the phase boundary assumes theshape of a surface curved convexly toward the single crystal. The extentof the curvature can be specified by a height h. This is the same as thedistance between the surface of the melt and the center of the phaseboundary. In the case of single crystals which are pulled according tothe invention, the curvature of the phase boundary is considerable. Thephase boundary may also be regarded as an isothermal surface, i.e. as asurface which is formed by points at which the same temperatureprevails. The concentration at which oxygen and dopants, for exampleboron, phosphorus, arsenic or antimony, are absorbed into the singlecrystal is sensitive to the temperature in the region of the phaseboundary. Inevitable temperature variations not only lead to the axialposition of the phase boundary varying by small amounts over the courseof time, but also to a take-up of oxygen and dopants into the singlecrystal which varies as a function of time. The different concentrationsof these elements can be revealed in the form of growth striations,which are formed according to the profile of the phase boundary. In aplan view of the semiconductor wafer, the growth striations appear asrings, and as curved lines in side view of a cross section through thesemiconductor wafer or through a longitudinal section through a piece ofthe single crystal. The profile of the attitude angle θ of these linesprovides information regarding the curvature of the phase boundary whenpulling the single crystal. Since single crystals with such a profile ofattitude angle can only be produced by the method according to theinvention, in so far as they deliver defect-free semiconductor wafers ofsilicon, the profile of the attitude angle θ is an unequivocal indicatorfor the application of the method according to the invention.

The invention therefore also relates to a semiconductor wafer of siliconwhich has neither OSF defects, nor A-swirl defects, nor COP defects witha size of more than 30 nm, with a radial profile of growth striations ofoxygen or dopants in which an attitude angle θ between a horizontal lineand the tangent applied to the growth striations lies within a range,expressed in degrees, described by the inequality θ<−17×(r/rmax) whenthe attitude angle θ is determined in a range of from r/rmax=0.1 tor/rmax=0.9, where r is the radial position at which the tangent isapplied to the growth striations and rmax denotes the radius of thesemiconductor wafer. A semiconductor wafer is therefore a semiconductorwafer according to the invention whenever there is at least one attitudeangle θ in the range of from r/rmax=0.1 to r/rmax=0.9, the value ofwhich falls within the value range specified by the inequality.

It is preferable for the attitude angle θ in the range of fromr/rmax=0.1 to r/rmax=0.9 to remain entirely in the aforementioned valuerange. According to a preferred embodiment, a semiconductor wafer istherefore a semiconductor wafer according to the invention if everyattitude angle θ in the range of from r/rmax=0.1 to r/rmax=0.9 lies inthe range specified by the inequality.

It is particularly preferable for the attitude angle θ in the range offrom r/rmax=0.1 to r/rmax=0.9 to remain entirely in a range which isdescribed by the modified inequality −50×(r/rmax)<θ<−17×(r/rmax).According to the particularly preferred definition, a semiconductorwafer is therefore a semiconductor wafer according to the invention ifevery attitude angle θ in the range of from r/rmax=0.1 to r/rmax=0.9lies in the range specified by the modified inequality.

FIG. 4 graphically represents the way in which semiconductor wafersaccording to the invention can differ from those of the prior art. Ifthe attitude angle θ is plotted against the radius of the semiconductorwafer, then it is only for semiconductor wafers according to theinvention that the resulting line lies in a zone that is described bythe specified inequality. The zone is restricted to radial positionsr/rmax of from 0.1 to 0.9, because the attitude angle θ in the adjoiningregions can not be determined accurately. For comparison, FIG. 4 alsoindicates the profile of the attitude angle θ obtained for semiconductorwafers which are produced according to the methods described in U.S.Pat. No. 6,869,478 B2 and DE 103 39 792 A1, respectively.

Besides oxygen and at least one dopant, the semiconductor wafersaccording to the invention preferably also contain at least one of theelements carbon, nitrogen and hydrogen. If nitrogen is present, then theconcentration is preferably from 2.0×10¹³ to 1.0×10¹⁵ atoms/cm³. Thepresence of carbon, nitrogen or both elements assists the formation ofBMDs and therefore improves getterability. It is thus particularlyadvantageous for the oxygen concentration to be comparatively low whenthese dopants are present. The presence of hydrogen hinders theformation of OSF defects, and thus makes it particularly advantageousfor the oxygen concentration to be comparatively high.

For controlling the radial profile of the ratio V/G according to theinvention, in principle any measure may be envisaged which is known tohave an effect on one of these parameters. Since there is littlelatitude for varying the pull rate owing to the criterion of having tobe able to pull as economically as possible and therefore as rapidly aspossible, most of these measures are aimed at adjusting the radialprofile of the temperature gradient G, particularly in the regions ofthe compressive and tensile stresses, according to the specifications ofthe invention. This is best achieved by suitably configuring andinfluencing the close vicinity of the single crystal, the so-called hotzone, and, accordingly, also by suitable measures for supplying heat tothe single crystal and dissipating heat from the single crystal.Measures which have been described in DE 103 39 792 A1 and U.S.published application US 2006/292890, both incorporated herein byreference for controlling the ratio V/G, for example, are particularlypreferred. An example particularly to be mentioned is the use of a heatsource, by which heat can be transported in a particular degree to thecenter of the phase boundary, and particularly in the configuration of aheater which is arranged below the crucible center and can be raised andlowered with the crucible. Such a heater is particularly preferred whenit generates a radial temperature profile at the crucible bottom, with apronounced temperature maximum at the center of the crucible bottom. Inaddition, the crucible bottom may be heated with the aid of a heatsource which is arranged statically under the crucible and is thereforenot raised together with the crucible when pulling the single crystal.

Together with a conventional side heater, which encloses the crucible,heat is thus preferably delivered to the melt in three ways. The desiredheat transport directed toward the center of the phase boundary may alsobe brought about by rotating the crucible and the single crystal in thesame sense, even though the increase of G thereby achieved is lesspronounced. By the additional use of magnetic fields, in particularhorizontal fields or CUSP fields or traveling magnetic fields, not onlycan the concentration of oxygen in the single crystal be limited, butalso an effect can be exerted on the heat transport. Thus, CUSP fieldsin particular are suitable as means for focusing a melt flow which isdirected upward toward the center of the phase boundary and transportsheat. This effect is particularly pronounced when the neutral plane ofthe CUSP field, where the CUSP field equates to an axisymmetrichorizontal field, lies at a distance above the surface of the melt whichis equal to at least 50 mm. A further instrument for increasing thetemperature gradient G is a cooler, which surrounds the single crystaland effectively dissipates heat from the single crystal. Likewisesuitable for controlling the temperature gradient G, but also forreducing thermomechanical stresses in the single crystal, is a heatsource which heats an edge of the single crystal adjoining the phaseboundary, most preferably in the configuration of an annular heatersurrounding the single crystal near the surface of the melt.

The annular heater and the cooler are preferably operated in such a waythat the axial temperature profile on the surface of the single crystalcan be described by a curve which has at least one point of inflexion,i.e. can be approximated by a polynomial of at least third order, andwhich therefore differs from the parabolic temperature profile describedin U.S. Pat. No. 6,869,478 B2. The preferred axial temperature profileis represented in FIG. 5. The single crystal is preferably not cooleduntil a distance above the surface of the melt which is greater than theheight h between the center of the phase boundary and the surface of themelt.

FIGS. 6 a and 6 b show a comparison of the radial profile of thetemperature gradient G and the strength of the thermomechanical stressfields, when, for the rapid pulling of large single crystals, on the onehand the strategy is adopted of keeping the radial profile of V/G ashomogeneous as possible and close to the critical ratio (FIG. 6 a), andon the other hand proceeding according to the invention (FIG. 6 b). Ifthe radial profile of V/G is configured homogeneously, then a region isformed in the single crystal with strongly pronounced compressivestresses, which adjoins a central zone of the phase boundary, and aregion with strongly pronounced tensile stresses which adjoins an edgeregion of the single crystal and the phase boundary. The consequence ofthis is that the ratio V/G adjusted to the critical ratio differssignificantly in both regions from the value which would be necessary inorder to avoid a defect-forming excess of intrinsic point defects. Incontrast to this, the different spacing of the isothermal lines in FIG.6 b shows that such a detrimental adjustment of the ratio V/G does nottake place with the method according to the invention. A hightemperature gradient G is adjusted in the region of the compressivestresses and a lower temperature gradient G in the region of the tensilestresses, as a result preventing a defect-forming excess of intrinsicpoint defects from being created. FIG. 6 b furthermore shows that thestrength of the stress fields is reduced by using the annular heater,and it is therefore easier to counteract their effect on the defectformation by adapting the radial profile of V/G according to theinvention. The height h is preferably at least 20 mm.

The oxygen concentration in the single crystal is also preferablycontrolled, so that no OSF defects are formed even if the single crystalis pulled under conditions which promote the formation of such defects.On the other hand, there should preferably be sufficient oxygen so thatenough nucleation centers are present for oxygen precipitates (BMDs). Aconcentration according to ASTM Standard F121-83 in the range of from5×10¹⁷ atoms/cm³ to 6.5×10¹⁷ atoms/cm³ is preferably adjusted. Theoxygen concentration is preferably controlled via the field strengthgenerated by the magnet coils, via the pressure in the pulling systemand via the flow rate per unit time with which an inert gas, for exampleargon, is fed through the pulling system, or by a combination of thesecontrol instruments. The oxygen content in the single crystal isdependent on the melt flows. With rotation of the single crystal and thecrucible in the same sense, for example, increased crucible rotationleads to a higher oxygen content. Field strengths of at least 10 mT(7960 A/m) to 80 mT (63700 A/m) in the melt are particularly preferredin the region of the pulling axis, as well as a pressure-flow rate ratioof from 0.004 to 0.03 mbar/(l/h).

Comparative Example

An attempt was made to pull a single crystal of silicon at a rate of0.64 mm/min, with the aim of obtaining as many defect-free semiconductorwafers as possible. In order to achieve this aim, the radial profile ofthe ratio V/G was controlled according to the strategy formulated in DE103 39 792 A1, i.e. to obtain a maximally homogeneous radial profilelying at the critical ratio. The maximum difference from the criticalratio was actually no more than 9%. With this strategy, however, nodefect-free semiconductor wafers could be obtained.

Example

In order to produce semiconductor wafers according to the invention, thesame device was used as in the comparative example.

The device represented in FIG. 7 comprised, a crucible 8 containing themelt and a side heater 6 surrounding the crucible, as well as a heatshield 2. The device furthermore contained two mutually oppositemagnetic field coils 5 which generated a CUSP magnetic field, and abottom heater 10 raisable with the crucible for transporting heat to thecenter of the phase boundary of the growing single crystal 9. Otherfeatures of the pulling device were a stationary bottom heater 7, acooler 1 surrounding the single crystal and cooled with water andblackened on the inner surface, as well as an annular heater 3.

A map, which reveals thermomechanical stress fields in the singlecrystal, was compiled for this hot zone with the aid of simulationcalculations. The aforementioned Flow Module program, whichtwo-dimensionally calculates the elastic stresses axisymmetrically andisotropically, was used as the simulation program. The calculations werebased on a Young's modulus of silicon, E=150 GPa, the Poisson ratiov=0.25 and the linear expansion coefficient α=2.6×10⁻⁶/K. As shown byFIG. 8, thermomechanical stresses of up to −26 MPa were found in theregion of the compressive stresses, and up to 7.53 MPa in the region ofthe tensile stresses. In order to take account of this observation, theradial profile of V/G was modified and adjusted according to therepresentation in FIG. 3, with a ratio (V/G)t/(V/G)c of approximately1.93 and (V/G)c /(V/G)crit of 0.7 and (V/G)t/(V/G)crit of 1.35 and with(V/G)crit being the critical ratio.

From the single crystal pulled under these conditions at a rate of 0.6mm/min, defect-free semiconductor wafers of silicon with a diameter of300 mm could be obtained with high yield. Neither A-swirl defects norFPD nor OSF defects could be detected on the silicon wafers. Theexamination for COP defects was carried out with a scattered laser lightmeter of the MO-4 type from Mitsui, Mining, the application of which isdescribed for example by Nakai et al. in Jap. Journal of AppliedPhysics, Vol. 43, No. 4A, 2004, pp. 1247-1253. No COP defects with adiameter of more than 30 nm were found.

FIGS. 9 a and 9 b show the result of a photoscan, by which the profileof the dopant striations was revealed. In this method, charge carriersare stimulated by laser light and detected electrically. FIG. 9 a showsthe side view of a panel-shaped longitudinal section through an 80 mmlong piece of the pulled single crystal. FIG. 9 b represents the way inwhich the radial profile of the attitude angle θ is established byevaluating the side view of a cross section through the semiconductorwafer. The radial profile established for the attitude angle θ in theexample corresponded to the profile represented in FIG. 4.

As an alternative or in addition to the evaluation of dopant striations,the radial profile of the attitude angle θ may also be established by asimilar evaluation of oxygen striations. The oxygen striations arerevealed by etching the fracture edge after the precipitation of oxygenby a heat treatment, and assessing it by oblique exposure to UV light.

While embodiments of the invention have been illustrated and described,it is not intended that these embodiments illustrate and describe allpossible forms of the invention. Rather, the words used in thespecification are words of description rather than limitation, and it isunderstood that various changes may be made without departing from thespirit and scope of the invention.

1. A semiconductor wafer of silicon which has neither OSF defects, norA-swirl defects, nor COP defects with a size of more than 30 nm, with aradial profile of growth striations of oxygen or dopants in which anattitude angle θ between a horizontal line and the tangent applied tothe growth striations lies in a range, expressed in degrees, describedby the inequality θ<−17×(r/rmax) when the attitude angle θ is determinedin a range of from r/rmax=0.1 to r/rmax=0.9, where r is the radialposition at which the tangent is applied to the growth striations andrmax denotes the radius of the semiconductor wafer.
 2. The semiconductorwafer of claim 1, wherein the attitude angle θ in the range of fromr/rmax=0.1 to r/rmax=0.9 lies without exception in the range ofθ<−17×(r/rmax).
 3. The semiconductor wafer of claim 1, wherein theattitude angle θ in the range of from r/rmax=0.1 to r/rmax=0.9 lieswithout exception in a subrange described by the inequality−50×(r/rmax)<θ<−17×(r/rmax).
 4. The semiconductor wafer of claim 1,further comprising at least one element selected from the groupconsisting of carbon, nitrogen and hydrogen.
 5. The semiconductor waferof claim 4, having a nitrogen concentration of from 2.0×10¹³ to 1.0×10¹⁵atoms/cm³.
 6. The semiconductor wafer of claim 1, having an oxygenconcentration of from 5×10¹⁷ atoms/cm³ to 6.5×10¹⁷ atoms/cm³.